Big question, wannago, and if it has to be one or the other, my choice would be your July – January slot.
October, November, December is the best desert weather, you can expect blue skies, moderate temperatures, but possibility of brief local rainfall in December.
January and February tend to be hazy.
March, April and May are windy with increasing likelihood of sand storms.
June, July, and August are very hot, tough on travellers and vehicles.
Hope this helps.
You could get some more scientific information from Country websites.
Kitmax - Traveller
Desert Pictures at